Gender is an identity and sex is a pasttime.
NO! Wait!
Sex is part of one's physiology. For the most part, this is male and female. But, there is more to it than that as intersex persons do indeed exist, too.
Gender is a bit more complicated. It seems to me (at this point) to be partially physical and partially constructed. I'm not an androgyne because I chose to be. But, how I "present" my androgyne gender identity is something I choose. Therefore, to me at least, the presentation of gender is constructed.